Species Distribution Models (SDM’s)

February 22, ’23

talk overview

Applications
Objectives
Methods
Interpretation

applications - conservation

aid in discovery of new populations of imperiled plants
aid in creation of reserves under climate change models
aid in predicting joint species distributions, i.e. obligate mutualisms

applications - academic

fine scale models to study co-existence
develop candidate species for metabarcoding

objectives

using known occurrences of a species, identify areas which have similar habitat and the potential to support populations

but, what about dispersal?

competition?

mutualisms?

an example species to accompany our study

Besseya (=Synthris) alpina (A. Gray) Rydberg.

American Basin

B. alpina, Franklin #3948

methods - overview

define spatial domain and grain

software environments

dependent variables

independent variables

modelling approaches

model evaluation

predicting a model into space

domain and grain

domain; spatial extent of study
- administrative boundary
- ecological model

grain; scales in space and time
- resolution at which process occurs (space)
- current and past climate (time)
- projected climates
- (animals) seasonal patterns?

limitation: compute power

The first few steps in your analysis is to reasonably define a few parameters. It is easy to get carried away when you do not have to collect field data yourself, and try to perform analyses at enormous spatial scales, or at very very fine details.

Remember the ‘domain’ is the spatial extent over which we are interested in studying a process. Generally, these are defined by funding agencies, e.g. for all of my normal office work, I use extents of land ownership; a form of administrative boundary. For academic work, depending on how the funding comes through, we may be much more likely to use domains informed by ecological processes. Examples would be a floristic province, or an ecoregion concept.

Grain is the resolution of an event in both time and space. For a spatial grain, you want to gather predictor variables which are able to correlate well with your species. For example day length in spring for plants, will only vary substantially over quite large scales. Elevation at a scale of 1 meter, rather than a more coarse surface would contain much meaningless variation. So we must balance these; however, most publicly available spatial data come only at a few resolutions (800m², 1000m², or 4000m²).

Temporal grain is very important for migratory animals, it is also very important if you want to see a species distribution before climate change effects, and after, and if you want to project your results into the future under climate change projections.

It sounds like you will have many options to sort through here, but no! You are informed by computer power, you do what you can, just like with fieldwork.

domain and grain

Domain

software environments

R
- caret data partitioning Kuhn (2022)
- sf vector data ala tidyverse Pebesma (2018)
- terra raster data without headaches Hijmans (2022)
- sdm modelling operations Naimi and Araujo (2016)
grass gis many modules for creating predictors
qgis graphical user interface for mouse guided visualization

There are a handful of options which exist for generating species distribution models and processing geographic information systems data. I can only advocate the use of open source software, as this allows others to benefit and reproduce our research without considerable fiscals resources. Furthermore, open source alternatives are generally much better than paid software. As species distribution models are really all about the statistics, R, is an un- paralled software to generate SDM’s in, and will keep your notes for you! However, grass gis offers several modules, all of which are accessible from the command line, which create useful spatial data products. Likewise QGIS is a really great lightweight GIS with a super friendly graphical user interface which you can use to visualize your predictor variables more dynamically than the experience offered by R and Rstudio.

We rely heavily on the sdm package, which is one of the best examples of object orientated programming which I have seen in R, and is capable of loading in statistical methods from nearly any R package you want! For example if you want any flavor of linear models you can import new methods from any Ben Bolker package you want!

dependent variables - presences

occurrences of a species in space (and time)
Linear models:
- check for spatial autocorrelation using Morans I
- sampling artefact? remove samples
- thin points piecewise by most offending record

dependent variables - presences example

Occurence Records

dependent variables - absences

optional: pseudoabsences space (and time)
more optional: absences space (and time)

presence:absence records
- linear models - 1:many
- machine learning - 1:1
distance between presences
- geographic
- environmental

dependent variables - absences example

just create some random red points and add em to the map above.

independent variables

variables relating to patterns in biotic distribution
- relevant to your extent and grains
- require variation
- no focus on factors governing biological processes, rather features which correlate with the known species distribution
limitation: compute power

independent variables - examples

domain: continental (e.g. North America)
- maximum and minimum daily temperatures [monthly, 4km]
- precipitation [monthly, 4km]
- hydrologic drainage [millenial, 4km]

domain: regional (e.g. Southern Rockies)
- elevation [millenial, 1km]
- soil classes [millenial, 1km]
- solar radiation [millenial, 1km]
- precipitation form [monthly, 1km]

domain: fine (e.g. McDonald Woods)
- micro topography [decade, 1m]
- water relations [decade, 1m]
- shade [weekly, 1m]
- soils [decade, 1m]

So as an example of how domain may affect our selection of independent variables, we can image we are interested in modelling species at three different levels. The first is across North America, we will probably have very good results using rather simple variables, at relatively coarse grains. For example, the maximum temperature - e.g. heat stress, and minimum temperatures are linked to the movement of moisture in plants and have enormous effects on distributions. Even the two sides of the Mississippi River Drainage basin, largely this an area so flat for nearly a thousand miles you cannot even detect changes in elevation or slope; might have the single largest effect on the flora of north america!

When we move to less extensive domains our predictors will change. We may start to gather very good information from toporgraphic relief, especially in the west; soil now be at a scale where it correlates with distributions at the class level, and solar radiation may start to tease out mesic north facing forested areas.

As we move to fine domains, and these really are the frontier for these models, especially in academic settings, we are really starting to get to very directly related features. Here we can really start to integrate field experiments, and nitty gritty natural history observations with species distribution models. Assuming you can find the spatial data to do so!

independent variables - specific examples

Percent bedrock (rocky, young soils)
Elevation (alpine habitat)
Bare ground (few others plants?)
X-Y coords (alpine zone decreases with latitude)
Soil surface pH (calcareous bedrock?)
Precipitation as snow (monsoonal influence?)

variance in independent variables

explicitly check for variation
carefully encode categorical data
too much, may not be useful
too little, may not be useful
pilot knock out studies; use one variable leaving the others out
warrants simplifying a variable?

modelling approaches - overview

ensembles pt. I & II
linear models
- assumptions - dependent variables (IV)
- assumptions - independent variables (DV)
- modelling
  - model evaluation
- machine learning
  - assumptions ?
  - modelling
    - model evaluation
ensembles pt. III

ensembles pt I

problems with all models
- garbage.(in) -> garbage.(out)
- influential outliers

with machine learning;
- models can fixate on these observations

solution:
- run many models, synthesize the results

“we are stronger together than we are alone” - Walter Payton

ensembles pt II

implementations:
- weak learners; many simple decision tree models are combined to a single output
  - bootstrap aggregation (bagging) e.g. random forests
    - many models run independent of each
  - boosting e.g. boosted regression trees
    - many models run sequentially, focusing on correcting errors in the last iteration
- stacking another form of combining many models
  - can accommodate the consensus output from bagged, boosted, or traditional linear models

linear models

commonly implemented:
- generalized linear models (glms)
- generalized additive models (gams)

linear models - assumptions DV

linear models - assumptions IV

Variance inflation
identify correlated variables
pilot knock out studies; use one variable leaving the others out

correlated!

modelling process

all evaluation performed by computer – too much information

machine learning

much more common approach than individual linear models

species distributions are generally too complex for individual predictors, and building fully interactive terms would take a long time.

the typical approach since the late 90’s

do the work for you

machine learning - assumptions

none, get a few observations, the more the merrier.

modelling

train/test split (partition data)

no free lunch
- no silver bullet machine learning algorithm
- each is able to work better than others under diverse circumstances
try many types of models, select some that work for your application
commonly implemented:
- random forest
- maximum entropy (maxent)
- boosting (brt)
- support vector model

evaluation I

\[ Accuracy = \frac{\text{correct classifications}}{\text{all classifications }} \] \[ Sensitivity = \frac{\text{true positives}}{\text{true positives + false negatives }} \] probability of the method giving a positive result when the test subject is positive.

\[ Specificity = \frac{\text{true negatives}}{\text{true negatives + false positives }} \] probability of the method giving a negative result when the test subject is negative

evaluation II

Area Under the ROC Curve (AUC)
True Skill Statistic (TSS)
- unequal sample sizes, i.e. evaluate many models at once
Cohen’s kappa

ensembles pt II

several r packages offer stacking of many models, based on your selection of evaluation criteria to weigh them
the ‘test’ partition of your data are used to evaluate this final model

predicting a model into space

any model, based on values present in gridded (raster) data can be predicted onto a new raster surface
each covariate in the model, is generally a single raster layer
r packages, such as terra, do all the work for you
accordingly, species distribution models create a map as a product

interpretation

percent suitability of habitat
of each cell - not proportion of cell
based on your model

interpretation - example

Occurence Records

tips and tricks

keep a lab notebook; this is bench science
always start models small (avoid computer crashes)
use strong and discrete directory organization
scratch paper, whiteboards, flowcharts
dynamic programming; import/export data
track code on github

objectives - recapped

using known occurrences of a species, identify areas which have similar habitat and the potential to support populations

mutualisms?

modelling two species together, joint-SDMs

competition?

using suitability surfaces to plant assemblages of species in field experiments’

but, what about dispersal?

using gridded surfaces to model the probability of dispersal from known to suitable habitat

conclusion

species distribution models are very simple!
fun introduction to simple machine learning
represent a hypothesis of the probability of suitable habitat
new avenues (J-SDM’s) can include mutualisms
stacked species (S-SDM’s) distributions for predicting ecological assemblies

contact info

- github/sagesteppe

some extra info

modelling resources

two hour discussion of the ‘sdm’ package by an author

large repository for high throughput modelling

large repository about spatial data in R

short activity using a sdm like process to teach spatial data

modelling ensemble learning

Ensemble learning utilizes many sets of trees, each tree being composed of many binary decisions, to create a single model. Each independent variable ( - or feature) may become a node on the tree - i.e. a location on the tree where a binary decision will move towards a predicted outcome. Each of the decision tree models which ensemble learning utilizes is a weak model, each of which may suffer due to high variance or bias, but which produce better outcomes than would be expected via chance. When ensembled these models generate a strong model, a model which should have more appropriately balanced variance and bias and predicts outcomes which are more strongly correlated with the expected values than the individual weak models.

modelling random forest

Random Forest (RF) the training data are continually bootstrap re-sampled, in combination with random subsets of features, to create nodes which attempt to optimally predict a known outcome. A large number of trees are then aggregated, via the most common predictions, to generate a final classification prediction tree. Each individual prediction tree is generated independently of the others.

modelling boosted regression trees

Boosted Regression Tree (BRT) (or Gradient Boosted tree) An initial tree is grown, and all other trees are derived sequentially from it, as each new tree is grown the errors in responses from the last tree are weighed more heavily so that the model focuses on selecting dependent variables which refine predictions. All response data and predictor variables are kept available to all trees.

citations

Hijmans, Robert J. 2022. Terra: Spatial Data Analysis. https://CRAN.R-project.org/package=terra.

Kuhn, Max. 2022. Caret: Classification and Regression Training. https://CRAN.R-project.org/package=caret.

Naimi, Babak, and Miguel B. Araujo. 2016. “Sdm: A Reproducible and Extensible r Platform for Species Distribution Modelling.” Ecography 39: 368–75. https://doi.org/10.1111/ecog.01881.

Pebesma, Edzer. 2018. “ Simple Features for R: Standardized Support for Spatial Vector Data.” The R Journal 10 (1): 439–46. https://doi.org/10.32614/RJ-2018-009.